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  2. Breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Breadth-first_search

    When working with graphs that are too large to store explicitly (or infinite), it is more practical to describe the complexity of breadth-first search in different terms: to find the nodes that are at distance d from the start node (measured in number of edge traversals), BFS takes O(b d + 1) time and memory, where b is the "branching factor ...

  3. Tree traversal - Wikipedia

    en.wikipedia.org/wiki/Tree_traversal

    By contrast, a breadth-first search will never reach the grandchildren, as it seeks to exhaust the children first. A more sophisticated analysis of running time can be given via infinite ordinal numbers ; for example, the breadth-first search of the depth 2 tree above will take ω ·2 steps: ω for the first level, and then another ω for the ...

  4. Lexicographic breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Lexicographic_breadth...

    The algorithm is called lexicographic breadth-first search because the order it produces is an ordering that could also have been produced by a breadth-first search, and because if the ordering is used to index the rows and columns of an adjacency matrix of a graph then the algorithm sorts the rows and columns into lexicographical order.

  5. Parallel breadth-first search - Wikipedia

    en.wikipedia.org/wiki/Parallel_breadth-first_search

    The breadth-first-search algorithm is a way to explore the vertices of a graph layer by layer. It is a basic algorithm in graph theory which can be used as a part of other graph algorithms. For instance, BFS is used by Dinic's algorithm to find maximum flow in a graph.

  6. Best-first search - Wikipedia

    en.wikipedia.org/wiki/Best-first_search

    Best-first search is a class of search algorithms which explores a graph by expanding the most promising node chosen according to a specified rule.. Judea Pearl described best-first search as estimating the promise of node n by a "heuristic evaluation function () which, in general, may depend on the description of n, the description of the goal, the information gathered by the search up to ...

  7. Strongly connected component - Wikipedia

    en.wikipedia.org/wiki/Strongly_connected_component

    The yellow directed acyclic graph is the condensation of the blue directed graph. It is formed by contracting each strongly connected component of the blue graph into a single yellow vertex. If each strongly connected component is contracted to a single vertex, the resulting graph is a directed acyclic graph, the condensation of G.

  8. Dijkstra's algorithm - Wikipedia

    en.wikipedia.org/wiki/Dijkstra's_algorithm

    Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers. It can be generalized to any graph where the edge weights are partially ordered, provided the subsequent labels (a subsequent label is produced when traversing an edge) are monotonically non-decreasing. [10] [11]

  9. Clique problem - Wikipedia

    en.wikipedia.org/wiki/Clique_problem

    A simple decision tree to detect the presence of a 3-clique in a 4-vertex graph. It uses up to 6 questions of the form "Does the red edge exist?", matching the optimal bound n(n − 1)/2. The (deterministic) decision tree complexity of determining a graph property is the number of questions of the form "Is there an edge between vertex u and ...